The basic idea is using GeoGraphics twice. This basically allows you to put any part of a map inside any geo polygon of another map.

The first GeoGraphics produces a rectangular map (in lat-lon coordinates; note the use of GeoProjection->"Equirectangular") with the exact lat-lon ranges corresponding to the region your are interested in (note the use of GeoRange->visible). The result is given as a GeoGraphics[Graphics[...], ...] object. We take the Graphics[...] and rasterize it as an Image with enough resolution.

Finally, with the second GeoGraphics, we take the resulting Image and place it inside the geo visible region using GeoStyling[{"GeoImage", image}]. Note the use of "GeoImage" (instead of the alternative "Image"); this is to project that image to the geo projection chosen by the second GeoGraphics.

If you have questions about the process, do not hesitate to ask.

Jose.

Try this:

visible = GeoVisibleRegion[{44.0519, -123.0867, Quantity[100, "Kilometers"]}];

states = GeoEntities[visible, "AdministrativeDivision1"];

geographics = GeoGraphics[{EdgeForm[Black], FaceForm[], Polygon[states]}, 
GeoBackground -> "ReliefMap", GeoRange -> visible, GeoProjection -> "Equirectangular"];

image = Rasterize[First[geographics], "Image", RasterSize -> 1000];

GeoGraphics[{GeoStyling[{"GeoImage", image}], EdgeForm[Black], visible}, GeoBackground -> None]